Question

1. Write the expression in simplified radical form. Show your work. 3 – 2√11/ 2 +√11

Answer 1

write it down again
you mean (3-2√11)/(2+√11) I guess
(3-2√11)(2-√11)/(2+√11)(2-√11)
(28-7√11)/(-7)
therefore the answer is √11-4

Answer 2

ANSWER


`√(11) - 4`


Step-by-step explanation

The given radical expression is


`(3 - 2 √(11) )/(2 + √(11) )`

We rationalize the radical expression by multiplying both the numerator and denominator by the conjugate of

`2 + √(11)`

which is


`2 - √(11)`

This will give us,


`(3 - 2 √(11) )/(2 + √(11) ) * (2 - √(11) )/(2 - √(11) )`



`((3 - 2 √(11))(2 - √(11) ) )/((2 + √(11))(2 - √(11) ) )`
We expand the numerator and also apply difference of two squares to the denominator.



`\frac{6 - 3 √(11) - 4 √(11) + 2(11)}{ {2}^(2) - { (√(11) )}^(2) }`

This simplifies to,



`(6- 3√(11) - 4 √(11) + 22)/( 4- 11)`



`(28- 7 √(11) )/( - 7)`


We now share the denominator for the numerators to obtain,



`- (28)/(7) + (7 √(11) )/(7)`

This finally gives,


`- 4 + √(11) = √(11) - 4`